More by Aimee S. A. Johnson

Abstract

Let $\overline{x} \in [0,1)^2$. In this paper we find the rate at which knowledge
about the partition elements $\overline{x}$ lies in for one sequence of
partitions determines the partition elements it lies in for another sequence of
partitions. This rate depends on the entropy of these partitions and the
geometry of their shapes, and gives a two-dimensional version of Lochs' theorem.